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Extensions 1→N→G→Q→1 with N=C10 and Q=C23×C6

Direct product G=N×Q with N=C10 and Q=C23×C6
dρLabelID
C24×C30480C2^4xC30480,1213

Semidirect products G=N:Q with N=C10 and Q=C23×C6
extensionφ:Q→Aut NdρLabelID
C10⋊(C23×C6) = D5×C23×C6φ: C23×C6/C22×C6 → C2 ⊆ Aut C10240C10:(C2^3xC6)480,1210

Non-split extensions G=N.Q with N=C10 and Q=C23×C6
extensionφ:Q→Aut NdρLabelID
C10.1(C23×C6) = C2×C6×Dic10φ: C23×C6/C22×C6 → C2 ⊆ Aut C10480C10.1(C2^3xC6)480,1135
C10.2(C23×C6) = D5×C22×C12φ: C23×C6/C22×C6 → C2 ⊆ Aut C10240C10.2(C2^3xC6)480,1136
C10.3(C23×C6) = C2×C6×D20φ: C23×C6/C22×C6 → C2 ⊆ Aut C10240C10.3(C2^3xC6)480,1137
C10.4(C23×C6) = C6×C4○D20φ: C23×C6/C22×C6 → C2 ⊆ Aut C10240C10.4(C2^3xC6)480,1138
C10.5(C23×C6) = C6×D4×D5φ: C23×C6/C22×C6 → C2 ⊆ Aut C10120C10.5(C2^3xC6)480,1139
C10.6(C23×C6) = C6×D4⋊2D5φ: C23×C6/C22×C6 → C2 ⊆ Aut C10240C10.6(C2^3xC6)480,1140
C10.7(C23×C6) = C3×D4⋊6D10φ: C23×C6/C22×C6 → C2 ⊆ Aut C101204C10.7(C2^3xC6)480,1141
C10.8(C23×C6) = C6×Q8×D5φ: C23×C6/C22×C6 → C2 ⊆ Aut C10240C10.8(C2^3xC6)480,1142
C10.9(C23×C6) = C6×Q8⋊2D5φ: C23×C6/C22×C6 → C2 ⊆ Aut C10240C10.9(C2^3xC6)480,1143
C10.10(C23×C6) = C3×Q8.10D10φ: C23×C6/C22×C6 → C2 ⊆ Aut C102404C10.10(C2^3xC6)480,1144
C10.11(C23×C6) = C3×D5×C4○D4φ: C23×C6/C22×C6 → C2 ⊆ Aut C101204C10.11(C2^3xC6)480,1145
C10.12(C23×C6) = C3×D4⋊8D10φ: C23×C6/C22×C6 → C2 ⊆ Aut C101204C10.12(C2^3xC6)480,1146
C10.13(C23×C6) = C3×D4.10D10φ: C23×C6/C22×C6 → C2 ⊆ Aut C102404C10.13(C2^3xC6)480,1147
C10.14(C23×C6) = Dic5×C22×C6φ: C23×C6/C22×C6 → C2 ⊆ Aut C10480C10.14(C2^3xC6)480,1148
C10.15(C23×C6) = C2×C6×C5⋊D4φ: C23×C6/C22×C6 → C2 ⊆ Aut C10240C10.15(C2^3xC6)480,1149
C10.16(C23×C6) = D4×C2×C30central extension (φ=1)240C10.16(C2^3xC6)480,1181
C10.17(C23×C6) = Q8×C2×C30central extension (φ=1)480C10.17(C2^3xC6)480,1182
C10.18(C23×C6) = C4○D4×C30central extension (φ=1)240C10.18(C2^3xC6)480,1183
C10.19(C23×C6) = C15×2+ 1+4central extension (φ=1)1204C10.19(C2^3xC6)480,1184
C10.20(C23×C6) = C15×2- 1+4central extension (φ=1)2404C10.20(C2^3xC6)480,1185

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